JAMB 2014 Mathematics · Question 10

If gt2 - k - w = 0, make g the subject of the formula

Options

A. $\frac{k + w}{t^2}$
B. $\frac{k - w}{t^2}$
C. $\frac{k + w}{t}$
D. $\frac{k - w}{t}$

Answer: A. $\frac{k + w}{t^2}$

Explanation written with AI and checked against the answer key

Analysis

The goal is to rearrange the equation $gt^2 - k - w = 0$ so that $g$ stands alone on one side of the equals sign. This is a classic algebraic manipulation problem often found in JAMB Mathematics.

Concept

To make a variable the subject of a formula, you must isolate it by performing inverse operations on both sides of the equation.

Move all terms not containing the target variable ( $g$ ) to the other side.
Divide by the coefficient of the target variable to leave it by itself.

Step-by-Step Solution

Step 1: Write down the original equation.

gt^2 - k - w = 0

Step 2: Move the terms $-k$ and $-w$ to the right side of the equation. When you move a term across the equals sign, its sign changes (from negative to positive).

gt^2 = k + w

Step 3: Isolate $g$ . Since $g$ is being multiplied by $t^2$ , you must divide both sides of the equation by $t^2$ to isolate $g$ .

\frac{gt^2}{t^2} = \frac{k + w}{t^2}

Step 4: Simplify.

g = \frac{k + w}{t^2}

Conclusion

Comparing our result to the given options, we can see that our derived formula matches option A.

Exam Tip

When moving terms across the equals sign, always remember the "Sign Flip" rule:

Addition becomes Subtraction ( $+$ becomes $-$ )
Subtraction becomes Addition ( $-$ becomes $+$ )
Multiplication becomes Division ( $\times$ becomes $\div$ )
Division becomes Multiplication ( $\div$ becomes $\times$ )

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